Log in

Roadmap of the iron-based superconductor Majorana platform

  • Invited Review
  • Special Topic: Recent Progress and Perspective on Topological Quantum Computing
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

With a series of recent breakthroughs, iron-based superconductors (FeSC) with a topological Dirac surface state are becoming a promising material platform for hosting Majorana zero modes, which we refer to as the iron-Majorana platform. This platform uniquely combines high-Tc superconductivity, a topological band structure, and electron correlations into a single material, successfully avoiding the difficulties of achieving intrinsic p-wave topological superconductors and superconductor/topological insulator heterojunction systems. The most important advantages of the iron-Majorana platform are its wide topological region and large quasiparticle gap, which provide strong topological protection for pure Majorana zero modes (MZMs). When the superconductor/topological insulator heterojunction systems, e.g., InAs/Al nanowire, have the controversies of being trivial Majorana-like states, the iron-Majorana platform, which possesses well-understood physics and clear experimental evidence of vortex MZMs, is more likely to be a true MZM. However, unlike the nanowire Majorana systems with clear theoretical proposals for braiding schemes, the iron-Majorana system has no concrete method for exchanging the vortex MZMs or constructing a topological qubit. In this article, we propose a roadmap of the future efforts required for more physical exploration and achieving the non-Abelian exchange statistics of MZMs based on the iron-Majorana platform.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. O. A. Awoga, J. Cayao, and A. M. Black-Schaffer, Phys. Rev. Lett. 123, 117001 (2019), ar**v: 1904.03783.

    Article  ADS  Google Scholar 

  2. C. X. Liu, J. D. Sau, T. D. Stanescu, and S. Das Sarma, Phys. Rev. B 96, 075161 (2017), ar**v: 1705.02035.

    Article  ADS  Google Scholar 

  3. J. Cayao, and A. M. Black-Schaffer, Phys. Rev. B 104, L020501 (2021), ar**v: 2011.10411.

    Article  ADS  Google Scholar 

  4. G. Kells, D. Meidan, and P. W. Brouwer, Phys. Rev. B 86, 100503 (2012), ar**v: 1207.3067.

    Article  ADS  Google Scholar 

  5. H. Pan, and S. Das Sarma, Phys. Rev. B 104, 054510 (2021), ar**v: 2102.07296.

    Article  ADS  Google Scholar 

  6. B. D. Woods, J. Chen, S. M. Frolov, and T. D. Stanescu, Phys. Rev. B 100, 125407 (2019), ar**v: 1902.02772.

    Article  ADS  Google Scholar 

  7. H. Pan, and S. Das Sarma, Phys. Rev. B 105, 115432 (2022), ar**v: 2110.07536.

    Article  ADS  Google Scholar 

  8. C. X. Liu, J. D. Sau, and S. Das Sarma, Phys. Rev. B 97, 214502 (2018), ar**v: 1803.05423.

    Article  ADS  Google Scholar 

  9. S. Das Sarma, and H. Pan, Phys. Rev. B 103, 195158 (2021), ar**v: 2103.05628.

    Article  ADS  Google Scholar 

  10. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008), ar**v: 0707.1889.

    Article  ADS  Google Scholar 

  11. F. Wilczek, Nat. Phys. 5, 614 (2009).

    Article  Google Scholar 

  12. J. Alicea, Rep. Prog. Phys. 75, 076501 (2012), ar**v: 1202.1293.

    Article  ADS  Google Scholar 

  13. C. W. J. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013).

    Article  ADS  Google Scholar 

  14. B. A. Bernevig, Topological Insulators and Topological Superconductors (Princeton University Press, Princeton, 2013).

    Book  MATH  Google Scholar 

  15. N. Read, and D. Green, Phys. Rev. B 61, 10267 (2000), ar**v: condmat/9906453.

    Article  ADS  Google Scholar 

  16. S. B. Chung, H. Bluhm, and E. A. Kim, Phys. Rev. Lett. 99, 197002 (2007), ar**v: 0705.2660.

    Article  ADS  Google Scholar 

  17. G. E. Volovik, Jetp Lett. 70, 609 (1999), ar**v: cond-mat/9909426.

    Article  ADS  Google Scholar 

  18. T. Senthil, and M. P. A. Fisher, Phys. Rev. B 61, 9690 (2000), ar**v: cond-mat/9906290.

    Article  ADS  Google Scholar 

  19. M. Stone, and R. Roy, Phys. Rev. B 69, 184511 (2004), ar**v: cond-mat/0308034.

    Article  ADS  Google Scholar 

  20. P. Zhang, K. Yaji, T. Hashimoto, Y. Ota, T. Kondo, K. Okazaki, Z. Wang, J. Wen, G. D. Gu, H. Ding, and S. Shin, Science 360, 182 (2018), ar**v: 1706.05163.

    Article  ADS  Google Scholar 

  21. P. Zhang, Z. Wang, X. Wu, K. Yaji, Y. Ishida, Y. Kohama, G. Dai, Y. Sun, C. Bareille, K. Kuroda, T. Kondo, K. Okazaki, K. Kindo, X. Wang, C. **, J. Hu, R. Thomale, K. Sumida, S. Wu, K. Miyamoto, T. Okuda, H. Ding, G. D. Gu, T. Tamegai, T. Kawakami, M. Sato, and S. Shin, Nat. Phys. 15, 41 (2019), ar**v: 1809.09977.

    Article  Google Scholar 

  22. D. Wang, L. Kong, P. Fan, H. Chen, S. Zhu, W. Liu, L. Cao, Y. Sun, S. Du, J. Schneeloch, R. Zhong, G. Gu, L. Fu, H. Ding, and H. J. Gao, Science 362, 333 (2018), ar**v: 1706.06074.

    Article  ADS  Google Scholar 

  23. L. Kong, S. Zhu, M. Papaj, H. Chen, L. Cao, H. Isobe, Y. **ng, W. Liu, D. Wang, P. Fan, Y. Sun, S. Du, J. Schneeloch, R. Zhong, G. Gu, L. Fu, H. J. Gao, and H. Ding, Nat. Phys. 15, 1181 (2019), ar**v: 1901.02293.

    Article  Google Scholar 

  24. S. Zhu, L. Kong, L. Cao, H. Chen, M. Papaj, S. Du, Y. **ng, W. Liu, D. Wang, C. Shen, F. Yang, J. Schneeloch, R. Zhong, G. Gu, L. Fu, Y. Y. Zhang, H. Ding, and H. J. Gao, Science 367, 189 (2020), ar**v: 1904.06124.

    Article  ADS  Google Scholar 

  25. W. Liu, L. Cao, S. Zhu, L. Kong, G. Wang, M. Papaj, P. Zhang, Y. B. Liu, H. Chen, G. Li, F. Yang, T. Kondo, S. Du, G. H. Cao, S. Shin, L. Fu, Z. Yin, H. J. Gao, and H. Ding, Nat. Commun. 11, 5688 (2020), ar**v: 1907.00904.

    Article  ADS  Google Scholar 

  26. W. Liu, Q. Hu, X. Wang, Y. Zhong, F. Yang, L. Kong, L. Cao, G. Li, Y. Peng, K. Okazaki, T. Kondo, C. **, J. Xu, H. J. Gao, and H. Ding, Quantum Front. 1, 20 (2022).

    Article  Google Scholar 

  27. K. T. Law, P. A. Lee, and T. K. Ng, Phys. Rev. Lett. 103, 237001 (2009), ar**v: 0907.1909.

    Article  ADS  Google Scholar 

  28. H. Pan, C. X. Liu, M. Wimmer, and S. Das Sarma, Phys. Rev. B 103, 214502 (2021).

    Article  ADS  Google Scholar 

  29. S. A. González, L. Melischek, O. Peters, K. Flensberg, K. J. Franke, and F. von Oppen, Phys. Rev. B 102, 045413 (2020), ar**v: 2102.04726.

    Article  ADS  Google Scholar 

  30. S. R. Elliott, and M. Franz, Rev. Mod. Phys. 87, 137 (2015), ar**v: 1403.4976.

    Article  ADS  Google Scholar 

  31. A. Y. Kitaev, Russ. Math. Surv. 52, 1191 (1997).

    Article  Google Scholar 

  32. A. Y. Kitaev, Ann. Phys. 303, 2 (2003).

    Article  ADS  Google Scholar 

  33. Q. Liu, C. Chen, T. Zhang, R. Peng, Y. J. Yan, C. H. P. Wen, X. Lou, Y. L. Huang, J. P. Tian, X. L. Dong, G. W. Wang, W. C. Bao, Q. H. Wang, Z. P. Yin, Z. X. Zhao, and D. L. Feng, Phys. Rev. X 8, 041056 (2018), ar**v: 1807.01278.

    Google Scholar 

  34. C. Chen, Q. Liu, T. Z. Zhang, D. Li, P. P. Shen, X. L. Dong, Z. X. Zhao, T. Zhang, and D. L. Feng, Chin. Phys. Lett. 36, 057403 (2019), ar**v: 1904.04623.

    Article  ADS  Google Scholar 

  35. L. Kong, L. Cao, S. Zhu, M. Papaj, G. Dai, G. Li, P. Fan, W. Liu, F. Yang, X. Wang, S. Du, C. **, L. Fu, H. J. Gao, and H. Ding, Nat. Commun. 12, 4146 (2021), ar**v: 2010.04735.

    Article  ADS  Google Scholar 

  36. J. X. Yin, Z. Wu, J. H. Wang, Z. Y. Ye, J. Gong, X. Y. Hou, L. Shan, A. Li, X. J. Liang, X. X. Wu, J. Li, C. S. Ting, Z. Q. Wang, J. P. Hu, P. H. Hor, H. Ding, and S. H. Pan, Nat. Phys. 11, 543 (2015), ar**v: 1403.1027.

    Article  Google Scholar 

  37. S. S. Zhang, J. X. Yin, G. Dai, L. Zhao, T. R. Chang, N. Shumiya, K. Jiang, H. Zheng, G. Bian, D. Multer, M. Litskevich, G. Chang, I. Belopolski, T. A. Cochran, X. Wu, D. Wu, J. Luo, G. Chen, H. Lin, F. C. Chou, X. Wang, C. **, R. Sankar, Z. Wang, and M. Z. Hasan, Phys. Rev. B 101, 100507 (2020).

    Article  ADS  Google Scholar 

  38. P. Fan, F. Yang, G. Qian, H. Chen, Y. Y. Zhang, G. Li, Z. Huang, Y. **ng, L. Kong, W. Liu, K. Jiang, C. Shen, S. Du, J. Schneeloch, R. Zhong, G. Gu, Z. Wang, H. Ding, and H. J. Gao, Nat. Commun. 12, 1348 (2021), ar**v: 2001.07376.

    Article  ADS  Google Scholar 

  39. C. Chen, K. Jiang, Y. Zhang, C. Liu, Y. Liu, Z. Wang, and J. Wang, Nat. Phys. 16, 536 (2020), ar**v: 2003.04539.

    Article  Google Scholar 

  40. R. Song, P. Zhang, and N. Hao, Phys. Rev. Lett. 128, 016402 (2022), ar**v: 2107.06558.

    Article  ADS  Google Scholar 

  41. X. Wu, X. Liu, R. Thomale, and C. X. Liu, Natl. Sci. Rev. 9, nwab087 (2022).

    Article  Google Scholar 

  42. K. H. Wong, M. R. Hirsbrunner, J. Gliozzi, A. Malik, B. Bradlyn, T. L. Hughes, and D. K. Morr, ar**v: 2210.15582.

  43. R. X. Zhang, W. S. Cole, and S. Das Sarma, Phys. Rev. Lett. 122, 187001 (2019), ar**v: 1812.10493.

    Article  ADS  Google Scholar 

  44. M. J. Gray, J. Freudenstein, S. Y. F. Zhao, R. O’Connor, S. Jenkins, N. Kumar, M. Hoek, A. Kopec, S. Huh, T. Taniguchi, K. Watanabe, R. Zhong, C. Kim, G. D. Gu, and K. S. Burch, Nano Lett. 19, 4890 (2019), ar**v: 1902.10723.

    Article  ADS  Google Scholar 

  45. L. Y. Kong, and H. Ding, Acta Phys. Sin. 69, 110301 (2020), ar**v: 2108.12850.

    Article  ADS  Google Scholar 

  46. L. Fu, and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008), ar**v: 0707.1692.

    Article  ADS  Google Scholar 

  47. M. X. Wang, C. Liu, J. P. Xu, F. Yang, L. Miao, M. Y. Yao, C. L. Gao, C. Shen, X. Ma, X. Chen, Z. A. Xu, Y. Liu, S. C. Zhang, D. Qian, J. F. Jia, and Q. K. Xue, Science 336, 52 (2012).

    Article  ADS  Google Scholar 

  48. J. P. Xu, C. Liu, M. X. Wang, J. Ge, Z. L. Liu, X. Yang, Y. Chen, Y. Liu, Z. A. Xu, C. L. Gao, D. Qian, F. C. Zhang, and J. F. Jia, Phys. Rev. Lett. 112, 217001 (2014), ar**v: 1312.3713.

    Article  ADS  Google Scholar 

  49. J. P. Xu, M. X. Wang, Z. L. Liu, J. F. Ge, X. Yang, C. Liu, Z. A. Xu, D. Guan, C. L. Gao, D. Qian, Y. Liu, Q. H. Wang, F. C. Zhang, Q. K. Xue, and J. F. Jia, Phys. Rev. Lett. 114, 017001 (2015), ar**v: 1312.7110.

    Article  ADS  Google Scholar 

  50. H. H. Sun, K. W. Zhang, L. H. Hu, C. Li, G. Y. Wang, H. Y. Ma, Z. A. Xu, C. L. Gao, D. D. Guan, Y. Y. Li, C. Liu, D. Qian, Y. Zhou, L. Fu, S. C. Li, F. C. Zhang, and J. F. Jia, Phys. Rev. Lett. 116, 257003 (2016), ar**v: 1603.02549.

    Article  ADS  Google Scholar 

  51. L. H. Hu, C. Li, D. H. Xu, Y. Zhou, and F. C. Zhang, Phys. Rev. B 94, 224501 (2016), ar**v: 1607.03449.

    Article  ADS  Google Scholar 

  52. R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010), ar**v: 1002.4033.

    Article  ADS  Google Scholar 

  53. Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010), ar**v: 1003.1145.

    Article  ADS  Google Scholar 

  54. A. C. Potter, and P. A. Lee, Phys. Rev. Lett. 105, 227003 (2010), ar**v: 1007.4569.

    Article  ADS  Google Scholar 

  55. P. Marra, and A. Nigro, J. Phys.-Condens. Matter 34, 124001 (2022), ar**v: 2112.00757.

    Article  ADS  Google Scholar 

  56. S. Gazibegovic, D. Car, H. Zhang, S. C. Balk, J. A. Logan, M. W. A. de Moor, M. C. Cassidy, R. Schmits, D. Xu, G. Wang, P. Krogstrup, R. L. M. Op het Veld, K. Zuo, Y. Vos, J. Shen, D. Bouman, B. Shojaei, D. Pennachio, J. S. Lee, P. J. van Veldhoven, S. Koelling, M. A. Verheijen, L. P. Kouwenhoven, C. J. Palmstraim, and E. P. A. M. Bakkers, Nature 548, 434 (2017), ar**v: 1705.01480.

    Article  ADS  Google Scholar 

  57. R. M. Lutchyn, E. P. A. M. Bakkers, L. P. Kouwenhoven, P. Krogstrup, C. M. Marcus, and Y. Oreg, Nat. Rev. Mater. 3, 52 (2018), ar**v: 1707.04899.

    Article  ADS  Google Scholar 

  58. A. C. Potter, and P. A. Lee, Phys. Rev. B 85, 094516 (2012), ar**v: 1201.2176.

    Article  ADS  Google Scholar 

  59. S. Manna, P. Wei, Y. **e, K. T. Law, P. A. Lee, and J. S. Moodera, Proc. Natl. Acad. Sci. USA 117, 8775 (2020), ar**v: 1911.03802.

    Article  ADS  Google Scholar 

  60. B. Braunecker, G. I. Japaridze, J. Klinovaja, and D. Loss, Phys. Rev. B 82, 045127 (2010), ar**v: 1004.0467.

    Article  ADS  Google Scholar 

  61. B. P. Truong, K. Agarwal, and T. Pereg-Barnea, Phys. Rev. B 107, 104516 (2023), ar**v: 2211.13849.

    Article  ADS  Google Scholar 

  62. S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani, Science 346, 602 (2014), ar**v: 1410.0682.

    Article  ADS  Google Scholar 

  63. S. Jeon, Y. **e, J. Li, Z. Wang, B. A. Bernevig, and A. Yazdani, Science 358, 772 (2017), ar**v: 1710.04662.

    Article  ADS  Google Scholar 

  64. X. L. Qi, T. L. Hughes, and S. C. Zhang, Phys. Rev. B 82, 184516 (2010), ar**v: 1003.5448.

    Article  ADS  Google Scholar 

  65. C. Z. Chen, J. J. He, D. H. Xu, and K. T. Law, Phys. Rev. B 98, 165439 (2018), ar**v: 1810.02661.

    Article  ADS  Google Scholar 

  66. Q. Yan, Y. F. Zhou, and Q. F. Sun, Phys. Rev. B 100, 235407 (2018), ar**v: 1912.03469.

    Article  ADS  Google Scholar 

  67. J. Shen, J. Lyu, J. Z. Gao, Y. M. **e, C. Z. Chen, C. Cho, O. Atanov, Z. Chen, K. Liu, Y. J. Hu, K. Y. Yip, S. K. Goh, Q. L. He, L. Pan, K. L. Wang, K. T. Law, and R. Lortz, Proc. Natl. Acad. Sci. USA 117, 238 (2020).

    Article  ADS  Google Scholar 

  68. M. Kayyalha, D. **ao, R. Zhang, J. Shin, J. Jiang, F. Wang, Y. F. Zhao, R. **ao, L. Zhang, K. M. Fijalkowski, P. Mandal, M. Winnerlein, C. Gould, Q. Li, L. W. Molenkamp, M. H. W. Chan, N. Samarth, and C. Z. Chang, Science 367, 64 (2020).

    Article  ADS  Google Scholar 

  69. S. D. Sarma, M. Freedman, and C. Nayak, npj Quantum Inf. 1, 1 (2015).

    Article  Google Scholar 

  70. T. Karzig, C. Knapp, R. M. Lutchyn, P. Bonderson, M. B. Hastings, C. Nayak, J. Alicea, K. Flensberg, S. Plugge, Y. Oreg, C. M. Marcus, and M. H. Freedman, Phys. Rev. B 95, 235305 (2017), ar**v: 1610.05289.

    Article  ADS  Google Scholar 

  71. D. Rainis, and D. Loss, Phys. Rev. B 85, 174533 (2012), ar**v: 1204.3326.

    Article  ADS  Google Scholar 

  72. T. Karzig, W. S. Cole, and D. I. Pikulin, Phys. Rev. Lett. 126, 057702 (2021), ar**v: 2004.01264.

    Article  ADS  Google Scholar 

  73. M. J. Lawler, K. Fujita, J. Lee, A. R. Schmidt, Y. Kohsaka, C. K. Kim, H. Eisaki, S. Uchida, J. C. Davis, J. P. Sethna, and E. A. Kim, Nature 466, 347 (2010), ar**v: 1007.3216.

    Article  ADS  Google Scholar 

  74. Z. Zhu, M. Papaj, X. A. Nie, H. K. Xu, Y. S. Gu, X. Yang, D. Guan, S. Wang, Y. Li, C. Liu, J. Luo, Z. A. Xu, H. Zheng, L. Fu, and J. F. Jia, Science 374, 1381 (2021), ar**v: 2010.02216.

    Article  ADS  Google Scholar 

  75. H. Zhao, H. Li, L. Dong, B. Xu, J. Schneeloch, R. Zhong, M. Fang, G. Gu, J. Harter, S. D. Wilson, Z. Wang, and I. Zeljkovic, Nat. Phys. 17, 903 (2021), ar**v: 2106.07543.

    Article  Google Scholar 

  76. L. Schneider, P. Beck, T. Posske, D. Crawford, E. Mascot, S. Rachel, R. Wiesendanger, and J. Wiebe, Nat. Phys. 17, 943 (2021), ar**v: 2104.11497.

    Article  Google Scholar 

  77. A. Galluzzi, K. Buchkov, E. Nazarova, V. Tomov, G. Grimaldi, A. Leo, S. Pace, and M. Polichetti, Eur. Phys. J. Spec. Top. 228, 725 (2019).

    Article  Google Scholar 

  78. J. Zhang, L. Jiao, Y. Chen, and H. Yuan, Front. Phys. 6, 463 (2011).

    Article  ADS  Google Scholar 

  79. C. L. Song, Y. Yin, M. Zech, T. Williams, M. M. Yee, G. F. Chen, J. L. Luo, N. L. Wang, E. W. Hudson, and J. E. Hoffman, Phys. Rev. B 87, 214519 (2013), ar**v: 1212.3240.

    Article  ADS  Google Scholar 

  80. C. J. van der Beek, S. Demirdis, M. Konczykowski, Y. Fasano, N. R. Cejas Bolecek, H. Pastoriza, D. Colson, and F. Rullier-Albenque, Phys. B-Cond. Matter 407, 1746 (2012).

    Article  ADS  Google Scholar 

  81. A. A. Abrikosov, Rev. Mod. Phys. 76, 975 (2004).

    Article  ADS  Google Scholar 

  82. G. Blatter, M. V. Feigel’Man, V. B. Geshkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).

    Article  ADS  Google Scholar 

  83. S. J. Singh, and P. Mele, Future Potential of New High Tc Iron-Based Superconductors, in Superconductivity (Springer, Cham, 2020).

    Google Scholar 

  84. M. Li, G. Li, L. Cao, X. Zhou, X. Wang, C. **, C. K. Chiu, S. J. Pennycook, Z. Wang, and H. J. Gao, Nature 606, 890 (2022), ar**v: 2206.04512.

    Article  ADS  Google Scholar 

  85. C. J. Bolech, and E. Demler, Phys. Rev. Lett. 98, 237002 (2007), ar**v: cond-mat/0607779.

    Article  ADS  Google Scholar 

  86. V. Perrin, M. Civelli, and P. Simon, Phys. Rev. B 104, L121406 (2021), ar**v: 2011.06893.

    Article  ADS  Google Scholar 

  87. D. E. Liu, M. Cheng, and R. M. Lutchyn, Phys. Rev. B 91, 081405 (2015), ar**v: 1409.3860.

    Article  ADS  Google Scholar 

  88. T. Jonckheere, J. Rech, A. Zazunov, R. Egger, A. L. Yeyati, and T. Martin, Phys. Rev. Lett. 122, 097003 (2019), ar**v: 1809.10527.

    Article  ADS  Google Scholar 

  89. Q. Chen, K. Q. Chen, and H. K. Zhao, J. Phys.-Condens. Matter 26, 315011 (2014).

    Article  Google Scholar 

  90. B. Zocher, and B. Rosenow, Phys. Rev. Lett. 111, 036802 (2013), ar**v: 1208.4092.

    Article  ADS  Google Scholar 

  91. K. H. Wong, E. Mascot, V. Madhavan, D. J. Van Harlingen, and D. K. Morr, Phys. Rev. B 105, L220504 (2022), ar**v: 2110.02238.

    Article  ADS  Google Scholar 

  92. A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, and H. Shtrikman, Nat. Phys. 8, 887 (2012), ar**v: 1205.7073.

    Article  Google Scholar 

  93. H. F. Lü, Z. Guo, S. S. Ke, Y. Guo, and H. W. Zhang, J. Appl. Phys. 117, 164312 (2015).

    Article  ADS  Google Scholar 

  94. Z. Wang, P. Zhang, G. Xu, L. K. Zeng, H. Miao, X. Xu, T. Qian, H. Weng, P. Richard, A. V. Fedorov, H. Ding, X. Dai, and Z. Fang, Phys. Rev. B 92, 115119 (2015), ar**v: 1506.06766.

    Article  ADS  Google Scholar 

  95. A. Chen, and M. Franz, Phys. Rev. B 93, 201105 (2016).

    Article  ADS  Google Scholar 

  96. S. Kobayashi, and M. Sato, Phys. Rev. Lett. 115, 187001 (2015), ar**v: 1504.07408.

    Article  ADS  Google Scholar 

  97. T. Hashimoto, S. Kobayashi, Y. Tanaka, and M. Sato, Phys. Rev. B 94, 014510 (2016), ar**v: 1604.05081.

    Article  ADS  Google Scholar 

  98. Y. Li, D. Wang, and C. Wu, New J. Phys. 15, 085002 (2013), ar**v: 1304.4268.

    Article  ADS  Google Scholar 

  99. Z. Yan, Phys. Rev. B 100, 205406 (2019).

    Article  ADS  Google Scholar 

  100. Y. Huang, and C. K. Chiu, Phys. Rev. B 98, 081412 (2018), ar**v: 1708.05724.

    Article  ADS  Google Scholar 

  101. Y. Tanaka, T. Sanno, T. Mizushima, and S. Fujimoto, Phys. Rev. B 106, 014522 (2022), ar**v: 2205.04057.

    Article  ADS  Google Scholar 

  102. M. Kheirkhah, Z. Y. Zhuang, J. Maciejko, and Z. Yan, Phys. Rev. B 105, 014509 (2022), ar**v: 2107.02811.

    Article  ADS  Google Scholar 

  103. E. J. König, and P. Coleman, Phys. Rev. Lett. 122, 207001 (2019), ar**v: 1901.03692.

    Article  ADS  Google Scholar 

  104. B. Fu, Z. A. Hu, C. A. Li, J. Li, and S. Q. Shen, Phys. Rev. B 103, L180504 (2021), ar**v: 2010.15633.

    Article  ADS  Google Scholar 

  105. S. Qin, L. Hu, C. Le, J. Zeng, F. Zhang, C. Fang, and J. Hu, Phys. Rev. Lett. 123, 027003 (2019), ar**v: 1901.04932.

    Article  ADS  Google Scholar 

  106. S. Qin, L. Hu, X. Wu, X. Dai, C. Fang, F. C. Zhang, and J. Hu, Sci. Bull. 64, 1207 (2019).

    Article  Google Scholar 

  107. L. H. Hu, X. Wu, C. X. Liu, and R. X. Zhang, Phys. Rev. Lett. 129, 277001 (2022), ar**v: 2110.11357.

    Article  Google Scholar 

  108. C. Ren, Z. S. Wang, H. Q. Luo, H. Yang, L. Shan, and H. H. Wen, Phys. Rev. Lett. 101, 257006 (2008).

    Article  ADS  Google Scholar 

  109. I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, Phys. Rev. Lett. 101, 057003 (2008), ar**v: 0803.2740.

    Article  ADS  Google Scholar 

  110. P. Richard, T. Qian, and H. Ding, J. Phys.-Condens. Matter 27, 293203 (2015), ar**v: 1503.07269.

    Article  Google Scholar 

  111. T. Hanaguri, S. Niitaka, K. Kuroki, and H. Takagi, Science 328, 474 (2010), ar**v: 1007.0307.

    Article  ADS  Google Scholar 

  112. C. Liu, Z. Wang, Y. Gao, X. Liu, Y. Liu, Q. H. Wang, and J. Wang, Phys. Rev. Lett. 123, 036801 (2019).

    Article  ADS  Google Scholar 

  113. M. Marciani, L. Fanfarillo, C. Castellani, and L. Benfatto, Phys. Rev. B 88, 214508 (2013), ar**v: 1306.5545.

    Article  ADS  Google Scholar 

  114. C. Platt, R. Thomale, C. Honerkamp, S. C. Zhang, and W. Hanke, Phys. Rev. B 85, 180502 (2012), ar**v: 1106.5964.

    Article  ADS  Google Scholar 

  115. J. Wang, Phys. Rev. B 98, 024519 (2018), ar**v: 1804.02790.

    Article  ADS  Google Scholar 

  116. C. X. Liu, D. E. Liu, F. C. Zhang, and C. K. Chiu, Phys. Rev. Appl. 12, 054035 (2019), ar**v: 1901.06083.

    Article  ADS  Google Scholar 

  117. T. Posske, C. K. Chiu, and M. Thorwart, Phys. Rev. Res. 2, 023205 (2020), ar**v: 1908.03576.

    Article  Google Scholar 

  118. H. Y. Ma, D. Guan, S. Wang, Y. Li, C. Liu, H. Zheng, and J. F. Jia, J. Phys. D-Appl. Phys. 54, 424003 (2021), ar**v: 2012.10014.

    Article  ADS  Google Scholar 

  119. X. Ma, C. J. O. Reichhardt, and C. Reichhardt, Phys. Rev. B 101, 024514 (2020), ar**v: 1910.07033.

    Article  ADS  Google Scholar 

  120. B. Lian, X. Q. Sun, A. Vaezi, X. L. Qi, and S. C. Zhang, Proc. Natl. Acad. Sci. USA 115, 10938 (2018), ar**v: 1712.06156.

    Article  ADS  MathSciNet  Google Scholar 

  121. K. Flensberg, F. von Oppen, and A. Stern, Nat. Rev. Mater. 6, 944 (2021), ar**v: 2103.05548.

    Article  ADS  Google Scholar 

  122. B. I. Halperin, Y. Oreg, A. Stern, G. Refael, J. Alicea, and F. von Oppen, Phys. Rev. B 85, 144501 (2012), ar**v: 1112.5333.

    Article  ADS  Google Scholar 

  123. J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, Nat. Phys. 7, 412 (2011), ar**v: 1006.4395.

    Article  Google Scholar 

  124. A. Paetznick, C. Knapp, N. Delfosse, B. Bauer, J. Haah, M. B. Hastings, and M. P. da Silva, PRX Quantum 4, 010310 (2023), ar**v: 2202.11829.

    Article  ADS  Google Scholar 

  125. S. Mi, D. I. Pikulin, M. Wimmer, and C. W. J. Beenakker, Phys. Rev. B 87, 241405 (2013), ar**v: 1304.1685.

    Article  ADS  Google Scholar 

  126. S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, Phys. Rev. Lett. 98, 010506 (2007), ar**v: quant-ph/0606101.

    Article  ADS  Google Scholar 

  127. J. C. Y. Teo, and C. L. Kane, Phys. Rev. Lett. 104, 046401 (2010), ar**v: 0909.4741.

    Article  ADS  Google Scholar 

  128. A. Stern, and E. Berg, Phys. Rev. Lett. 122, 107701 (2019), ar**v: 1810.01200.

    Article  ADS  Google Scholar 

  129. L. H. Wu, Q. F. Liang, and X. Hu, Sci. Tech. Adv. Mater. 15, 064402 (2014).

    Article  Google Scholar 

  130. S. Vijay, and L. Fu, Phys. Rev. B 94, 235446 (2016), ar**v: 1609.00950.

    Article  ADS  Google Scholar 

  131. D. J. Clarke, J. D. Sau, and S. Das Sarma, Phys. Rev. B 95, 155451 (2017), ar**v: 1610.08958.

    Article  ADS  Google Scholar 

  132. S. Kezilebieke, M. N. Huda, V. Vaňo, M. Aapro, S. C. Ganguli, O. J. Silveira, S. Głodzik, A. S. Foster, T. Ojanen, and P. Liljeroth, Nature 588, 424 (2020), ar**v: 2002.02141.

    Article  ADS  Google Scholar 

  133. Q. Zhang, Z. Zhang, Z. Zhu, U. Schwingenschlögl, and Y. Cui, ACS Nano 6, 2345 (2012).

    Article  Google Scholar 

  134. J. Peng, C. Song, F. Li, B. Cui, H. Mao, Y. Wang, G. Wang, and F. Pan, ACS Appl. Mater. Interfaces 7, 17700 (2015).

    Article  Google Scholar 

  135. R. X. Zhang, W. S. Cole, X. Wu, and S. Das Sarma, Phys. Rev. Lett. 123, 167001 (2019).

    Article  ADS  Google Scholar 

  136. Z. Yan, F. Song, and Z. Wang, Phys. Rev. Lett. 121, 096803 (2018), ar**v: 1803.08545.

    Article  ADS  Google Scholar 

  137. K. Laubscher, D. Chughtai, D. Loss, and J. Klinovaja, Phys. Rev. B 102, 195401 (2020), ar**v: 2007.13579.

    Article  ADS  Google Scholar 

  138. W. A. Benalcazar, and A. Cerjan, Phys. Rev. Lett. 128, 127601 (2022), ar**v: 2109.06892.

    Article  ADS  Google Scholar 

  139. T. Liu, J. J. He, and F. Nori, Phys. Rev. B 98, 245413 (2018), ar**v: 1806.07002.

    Article  ADS  Google Scholar 

  140. X. Zhu, Phys. Rev. B 97, 205134 (2018), ar**v: 1802.00270.

    Article  ADS  Google Scholar 

  141. S. S. Qin, Z. Zhang, Y. Wang, C. Fang, F.-C. Zhang, and J. Hu, ar**v: 2208.10225.

  142. L. Chen, B. Liu, G. Xu, and X. Liu, Phys. Rev. Res. 3, 023166 (2021), ar**v: 1909.10402.

    Article  Google Scholar 

  143. J. J. He, T. Liang, Y. Tanaka, and N. Nagaosa, Commun. Phys. 2, 149 (2019), ar**v: 1901.04635.

    Article  Google Scholar 

  144. R. Peng, H. C. Xu, S. Y. Tan, H. Y. Cao, M. **a, X. P. Shen, Z. C. Huang, C. H. P. Wen, Q. Song, T. Zhang, B. P. **e, X. G. Gong, and D. L. Feng, Nat. Commun. 5, 5044 (2014).

    Article  ADS  Google Scholar 

  145. B. Landgraf, Structural, Magnetic and Electrical Investigation of Iron-Based III/V-Semiconductor Hybrid Structures, Dissertation for Doctoral Degree (Staats-und Universitätsbibliothek Hamburg Carl von Ossietzky, Hamburg, 2014).

    Google Scholar 

  146. X. L. Peng, Y. Li, X. X. Wu, H. B. Deng, X. Shi, W. H. Fan, M. Li, Y. B. Huang, T. Qian, P. Richard, J. P. Hu, S. H. Pan, H. Q. Mao, Y. J. Sun, and H. Ding, Phys. Rev. B 100, 155134 (2019), ar**v: 1903.05968.

    Article  ADS  Google Scholar 

  147. Q. Zou, Z. Ge, C. Yan, H. Zhang, and L. Li, Bull. Am. Phys. Soc. 65, 1 (2020).

    Google Scholar 

  148. M. Chen, X. Chen, H. Yang, Z. Du, and H. H. Wen, Sci. Adv. 4, eaat1084 (2018), ar**v: 1804.09319.

    Article  ADS  Google Scholar 

  149. B. Guo, K. G. Shi, H. L. Qin, L. Zhou, W. Q. Chen, F. Ye, J. W. Mei, H. T. He, T. L. Pan, and G. Wang, Chin. Phys. B 29, 097403 (2020).

    Article  ADS  Google Scholar 

  150. A. V. Putilov, C. Di Giorgio, V. L. Vadimov, D. J. Trainer, E. M. Lechner, J. L. Curtis, M. Abdel-Hafiez, O. S. Volkova, A. N. Vasiliev, D. A. Chareev, G. Karapetrov, A. E. Koshelev, A. Y. Aladyshkin, A. S. Mel’nikov, and M. Iavarone, Phys. Rev. B 99, 144514 (2019).

    Article  ADS  Google Scholar 

  151. P. Choubey, S. H. Joo, K. Fujita, Z. Du, S. D. Edkins, M. H. Hamidian, H. Eisaki, S. Uchida, A. P. Mackenzie, J. Lee, J. C. S. Davis, and P. J. Hirschfeld, Proc. Natl. Acad. Sci. USA 117, 14805 (2020), ar**v: 2002.11654.

    Article  ADS  Google Scholar 

  152. C. K. Chiu, T. Machida, Y. Huang, T. Hanaguri, and F. C. Zhang, Sci. Adv. 6, eaay0443 (2020), ar**v: 1904.13374.

    Article  ADS  Google Scholar 

  153. T. Machida, Y. Sun, S. Pyon, S. Takeda, Y. Kohsaka, T. Hanaguri, T. Sasagawa, and T. Tamegai, Nat. Mater. 18, 811 (2019), ar**v: 1812.08995.

    Article  ADS  Google Scholar 

  154. E. Bellingeri, S. Kawale, F. Caglieris, V. Braccini, G. Lamura, L. Pellegrino, A. Sala, M. Putti, C. Ferdeghini, A. Jost, U. Zeitler, C. Tarantini, and J. Jaroszynski, Supercond. Sci. Technol. 27, 044007 (2014).

    Article  ADS  Google Scholar 

  155. X. Chen, M. Chen, W. Duan, H. Yang, and H. H. Wen, Nano Lett. 20, 2965 (2020), ar**v: 1905.05735.

    Article  ADS  Google Scholar 

  156. C. Li, X. Luo, L. Chen, D. E. Liu, F.-C. Zhang, and X. Liu, ar**v: 2107.11562.

  157. L. Sang, Z. Li, G. Yang, M. Nadeem, L. Wang, Q. Xue, A. R. Hamilton, and X. Wang, Matter 5, 1734 (2022).

    Article  Google Scholar 

  158. H. Liu, M. Lu, Y. Wu, J. Liu, and X. C. **e, Phys. Rev. B 106, 064505 (2022), ar**v: 2111.11731.

    Article  ADS  Google Scholar 

  159. S. Rubbert, and A. R. Akhmerov, Phys. Rev. B 94, 115430 (2016).

    Article  ADS  Google Scholar 

  160. R. López, M. Lee, L. Serra, and J. S. Lim, Phys. Rev. B 89, 205418 (2014), ar**v: 1310.6282.

    Article  ADS  Google Scholar 

  161. C. Benjamin, and J. K. Pachos, Phys. Rev. B 81, 085101 (2010), ar**v: 0908.0655.

    Article  ADS  Google Scholar 

  162. K. Flensberg, Phys. Rev. Lett. 106, 090503 (2011), ar**v: 1011.5467.

    Article  ADS  Google Scholar 

  163. J. D. Sau, D. J. Clarke, and S. Tewari, Phys. Rev. B 84, 094505 (2011).

    Article  ADS  Google Scholar 

  164. S. Pagano, N. Martucciello, E. Enrico, E. Monticone, K. Iida, and C. Barone, Nanomaterials 10, 862 (2020).

    Article  Google Scholar 

  165. P. Yuan, Z. Xu, C. Li, B. Quan, J. Li, C. Gu, and Y. Ma, Supercond. Sci. Technol. 31, 025002 (2017), ar**v: 1711.07637.

    Article  ADS  Google Scholar 

  166. J. Liu, W. Cui, H. Wang, D. Zhao, B. Zuo, Y. Zhu, X. Liu, Z. Zhang, B. Sun, L. Wang, H. Chang, K. He, Q. K. Xue, and H. Liu, Supercond. Sci. Technol. 35, 065010 (2022).

    Article  ADS  Google Scholar 

  167. P. Liu, J. R. Williams, and J. J. Cha, Nat. Rev. Mater. 4, 479 (2019).

    Article  ADS  Google Scholar 

  168. Y. R. Tao, L. Fan, Z. Y. Wu, X. C. Wu, and Z. H. Wang, J. Alloys Compd. 751, 20 (2018).

    Article  Google Scholar 

  169. S. Mishra, K. Song, J. A. Koza, and M. Nath, ACS Nano 7, 1145 (2013).

    Article  Google Scholar 

  170. J. Alicea, Phys. Rev. B 81, 125318 (2010), ar**v: 0912.2115.

    Article  ADS  Google Scholar 

  171. D. Aasen, M. Hell, R. V. Mishmash, A. Higginbotham, J. Danon, M. Leijnse, T. S. Jespersen, J. A. Folk, C. M. Marcus, K. Flensberg, and J. Alicea, Phys. Rev. X 6, 031016 (2016), ar**v: 1511.05153.

    Google Scholar 

  172. S. Plugge, A. Rasmussen, R. Egger, and K. Flensberg, New J. Phys. 19, 012001 (2017), ar**v: 1609.01697.

    Article  ADS  Google Scholar 

  173. V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Science 336, 1003 (2012), ar**v: 1204.2792.

    Article  ADS  Google Scholar 

  174. P. P. Aseev, J. Klinovaja, and D. Loss, Phys. Rev. B 98, 155414 (2018), ar**v: 1807.07997.

    Article  ADS  Google Scholar 

  175. M. T. Deng, S. Vaitiekėnas, E. B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygård, P. Krogstrup, and C. M. Marcus, Science 354, 1557 (2016), ar**v: 1612.07989.

    Article  ADS  Google Scholar 

  176. H. Zhang, D. E. Liu, M. Wimmer, and L. P. Kouwenhoven, Nat. Commun. 10, 5128 (2019), ar**v: 1905.07882.

    Article  ADS  Google Scholar 

  177. B. Lei, N. Z. Wang, C. Shang, F. B. Meng, L. K. Ma, X. G. Luo, T. Wu, Z. Sun, Y. Wang, Z. Jiang, B. H. Mao, Z. Liu, Y. J. Yu, Y. B. Zhang, and X. H. Chen, Phys. Rev. B 95, 020503 (2017), ar**v: 1609.07726.

    Article  ADS  Google Scholar 

  178. P. Liu, B. Lei, X. Chen, L. Wang, and X. Wang, Nat. Rev. Phys. 4, 336 (2022).

    Article  Google Scholar 

  179. B. Lei, J. H. Cui, Z. J. **ang, C. Shang, N. Z. Wang, G. J. Ye, X. G. Luo, T. Wu, Z. Sun, and X. H. Chen, Phys. Rev. Lett. 116, 077002 (2016), ar**v: 1509.00620.

    Article  ADS  Google Scholar 

  180. Y. Cui, G. Zhang, H. Li, H. Lin, X. Zhu, H. H. Wen, G. Wang, J. Sun, M. Ma, Y. Li, D. Gong, T. **e, Y. Gu, S. Li, H. Luo, P. Yu, and W. Yu Sci. Bull. 63, 11 (2018), ar**v: 1712.01191.

    Article  Google Scholar 

  181. L. Cao, W. Liu, G. Li, G. Dai, Q. Zheng, Y. Wang, K. Jiang, S. Zhu, L. Huang, L. Kong, F. Yang, X. Wang, W. Zhou, X. Lin, J. Hu, C. **, H. Ding, and H. J. Gao, Nat. Commun. 12, 6312 (2021), ar**v: 2101.02427.

    Article  ADS  Google Scholar 

  182. V. V. Dremov, S. Y. Grebenchuk, A. G. Shishkin, D. S. Baranov, R. A. Hovhannisyan, O. V. Skryabina, N. Lebedev, I. A. Golovchanskiy, V. I. Chichkov, C. Brun, T. Cren, V. M. Krasnov, A. A. Golubov, D. Roditchev, and V. S. Stolyarov, Nat. Commun. 10, 4009 (2019).

    Article  ADS  Google Scholar 

  183. J. Y. Ge, V. N. Gladilin, J. Tempere, J. Devreese, and V. V. Moshchalkov, Nano Lett. 17, 5003 (2017).

    Article  ADS  Google Scholar 

  184. J. Y. Ge, V. N. Gladilin, J. Tempere, C. Xue, J. T. Devreese, J. van de Vondel, Y. Zhou, and V. V. Moshchalkov, Nat. Commun. 7, 13880 (2016), ar**v: 1701.06316.

    Article  ADS  Google Scholar 

  185. E. W. J. Straver, J. E. Hoffman, O. M. Auslaender, D. Rugar, and K. A. Moler, Appl. Phys. Lett. 93, 172514 (2008), ar**v: 0810.0790.

    Article  ADS  Google Scholar 

  186. B. van Heck, A. R. Akhmerov, F. Hassler, M. Burrello, and C. W. J. Beenakker, New J. Phys. 14, 035019 (2012), ar**v: 1111.6001.

    Article  ADS  Google Scholar 

  187. S. Nadj-Perge, I. K. Drozdov, B. A. Bernevig, and A. Yazdani, Phys. Rev. B 88, 020407 (2013).

    Article  ADS  Google Scholar 

  188. X. Liu, X. Li, D. L. Deng, X. J. Liu, and S. Das Sarma, Phys. Rev. B 94, 014511 (2016), ar**v: 1602.08093.

    Article  ADS  Google Scholar 

  189. J. P. T. Stenger, and R. S. K. Mong, Phys. Rev. A 101, 042338 (2020), ar**v: 1906.01658.

    Article  ADS  MathSciNet  Google Scholar 

  190. R. Radgohar, and M. Kargarian, Phys. Rev. B 102, 165111 (2020), ar**v: 2006.10577.

    Article  ADS  Google Scholar 

  191. D. Vincenzo, and D. Majorana, in Particles with noise: Problems with braiding anyons. Proceedings of the 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC, Brussels, 2015).

    Google Scholar 

  192. F. L. Pedrocchi, and D. P. DiVincenzo, Phys. Rev. Lett. 115, 120402 (2015), ar**v: 1505.03712.

    Article  ADS  Google Scholar 

  193. X. Luo, Y. He, T. F. J. Poon, X. Liu, and X.-J. Liu, ar**v: 1803.02173.

  194. S. Manna, A. Kamlapure, L. Cornils, T. Hänke, E. M. J. Hedegaard, M. Bremholm, B. B. Iversen, P. Hofmann, J. Wiebe, and R. Wiesendanger, Nat. Commun. 8, 14074 (2017), ar**v: 1606.03249.

    Article  ADS  Google Scholar 

  195. Y. Zhang, J. Huang, C. Zhang, P. Wang, Z. Wang, T. Wang, Z. **ng, and D. Y. **ng, Phys. Rev. B 102, 064503 (2020).

    Article  ADS  Google Scholar 

  196. S. B. Zhang, A. Calzona, and B. Trauzettel, Phys. Rev. B 102, 100503 (2020), ar**v: 2003.04053.

    Article  ADS  Google Scholar 

  197. R. Seoane Souto, and M. Leijnse, Scipost Phys. 12, 161 (2022).

    Article  ADS  Google Scholar 

  198. C. Beenakker, A. Grabsch, and Y. Herasymenko, Scipost Phys. 6, 022 (2019), ar**v: 1812.01444.

    Article  ADS  Google Scholar 

  199. L. Qin, X. Q. Li, A. Shnirman, and G. Schön, New J. Phys. 21, 043027 (2019), ar**v: 1901.08312.

    Article  ADS  MathSciNet  Google Scholar 

  200. Z. T. Zhang, and D. E. Liu, Phys. Rev. B 103, 195401 (2021), ar**v: 2012.05785.

    Article  ADS  Google Scholar 

  201. F. Borsoi, K. Zuo, S. Gazibegovic, R. L. M. Op het Veld, E. P. A. M. Bakkers, L. P. Kouwenhoven, and S. Heedt, Nat. Commun. 11, 1 (2020), ar**v: 2006.14645.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hong Ding.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 11888101), and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB28000000).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, W., Ding, H. Roadmap of the iron-based superconductor Majorana platform. Sci. China Phys. Mech. Astron. 66, 267002 (2023). https://doi.org/10.1007/s11433-022-2063-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-022-2063-7

PACS number(s)

Navigation